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A190676 [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(3),3,0) and [ ]=floor.

%I A190676 #9 Mar 25 2013 11:57:33
%S A190676 2,1,0,2,1,1,0,2,1,0,0,2,1,0,2,2,1,0,2,1,1,0,2,1,0,0,2,1,0,2,2,1,0,2,
%T A190676 1,1,0,2,1,0,0,2,1,0,2,2,1,0,2,1,1,0,2,1,0,2,2,1,0,2,1,1,0,2,1,0,0,2,
%U A190676 1,0,2,2,1,0,2,1,1,0,2,1,0,0,2,1,0,2,2,1,0,2,1,1,0,2,1,0,0,2,1,0,2,2,1,0,2,1,0,0,2,1,0,2,2,1,0,2,1,1,0,2,1,0,0,2,1,0,2,2,1,0,2,1
%N A190676 [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(3),3,0) and [ ]=floor.
%C A190676 Write a(n)=[(bn+c)r]-b[nr]-[cr].  If r>0 and b and c are integers satisfying b>=2 and 0<=c<=b-1, then 0<=a(n)<=b.  The positions of 0 in the sequence a are of interest, as are the position sequences for 1,2,...,b.  These b+1 position sequences comprise a partition of the positive integers.
%C A190676 Examples:
%C A190676 (golden ratio,2,1):  A190427-A190430
%C A190676 (sqrt(2),2,0):  A190480-A190482
%C A190676 (sqrt(2),2,1):  A190483-A190486
%C A190676 (sqrt(2),3,0):  A190487-A190490
%C A190676 (sqrt(2),3,1):  A190491-A190495
%C A190676 (sqrt(2),3,2):  A190496-A190500
%C A190676 (sqrt(2),4,c):  A190544-A190566
%F A190676 a(n)=[3n*sqrt(3)]-3[n*sqrt(3)].
%t A190676 r = Sqrt[3]; b = 3; c = 0;
%t A190676 f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
%t A190676 t = Table[f[n], {n, 1, 200}] (* A190676 *)
%t A190676 Flatten[Position[t, 0]]      (* A190677 *)
%t A190676 Flatten[Position[t, 1]]      (* A190678 *)
%t A190676 Flatten[Position[t, 2]]      (* A190679 *)
%t A190676 Table[Floor[3n Sqrt[3]]-3Floor[n Sqrt[3]],{n,140}] (* _Harvey P. Dale_, Mar 24 2013 *)
%Y A190676 Cf. A190677, A190678, A190679, A022838.
%K A190676 nonn
%O A190676 1,1
%A A190676 _Clark Kimberling_, May 16 2011
%E A190676 Definition (Name) corrected by _Harvey P. Dale_, Mar 24 2013